The second harmonic of a light beam can be generated efficiently only under particular conditions. A dipolar polarization oscillating at the second harmonic can be generated only in noncentrosymmetric materials; moreover, material dispersion limits the propagation length along which the second-harmonic light that is generated at each point can interfere constructively with that generated at neighboring points. The most straightforward way to address this problem of “phase matching” is the use of birefringent crystals. In these crystals, either the temperature or the angle of propagation with respect to the crystal’s axis can be tuned so that birefringence compensates exactly for material dispersion. A more sophisticated approach, called “quasi-phase matching,” enables the use of materials that cannot be phase matched using birefringence; in this approach, a crystal is arranged as a series of layers with alternating crystalline structure orientation; if the period of the structure is chosen correctly, the second-harmonic light produced at a given layer, whose phase depends on the crystal’s orientation, always interferes constructively with that produced at other layers along the direction of propagation of the beam at the fundamental frequency.

A new and surprising possibility is second-harmonic generation (SHG) from a silica nanowire, observed, for example, by Grubsky and Feinberg, Opt. Commun. 274, 447 (2007): silica is, in fact, centrosymmetric, so that the second harmonic can be generated in the bulk only from multipolar polarization and from dipolar polarization only at the surfaces. The SHG observed in doped silica fibers in experiments performed in the 1980s has been attributed to a material modification of silica, induced by multiphoton interactions, that renders it noncentrosymmetric and therefore allows a dipole second-order susceptibility. However, the fast rise time of the second-harmonic signal rules out this mechanism for the recent results in silica nanowires. The remaining explanation, supported by calculations, is that SHG at visible frequencies is due to bulk multipolar and surface dipolar nonlinearities and that the efficiency is high because the second-order interaction in these fibers is phase matched when both the fundamental and the second harmonic propagate in low-order modes that therefore have a good mutual overlap; material dispersion is in this case compensated by modal dispersion. This possibility of phase matching does not exist for visible wavelengths in a core cladding optical fiber in which the modal dispersion is not sufficient to compensate the material dispersion between the fundamental and the upconverted wave (in this case phase matching works for micrometer wavelengths in which material dispersion is smaller).

The observation that SHG in silica nanowires is not caused by a material modification has an immediate and important consequence. It has been impossible, in fact, to increase the efficiency of “material-modification induced” SHG above a few percent, and this limitation has been explained in a convincing way in the literature as a self-saturation of the material modification. On the other hand, there is no process that can limit in line of principle the conversion efficiency from phase matched “direct” SHG. The low cost of a silica nanowire makes this possibility very attractive.

The work by J. Lægsgaard provides a systematic and careful study of the practical limitations of this approach. Nanowires for high conversion efficiency must be quite long (on the order of several centimeters), so that the phase-matching bandwidth is narrow (on the order of tens of picometers— that supports pulses not shorter than a few tens of picoseconds); the work identifies therefore the phase mismatch that is necessarily created in various portion of the fiber by structural imperfections as the major obstacle to efficient conversion. Simulations on fluctuating structures whose geometry has random fluctuations across their length show that the precision with which fibers must be fabricated to achieve 10% conversion efficiency is beyond the present technological possibilities. The conclusion is that, at the present moment, the only way to convert light into its second harmonic with a nanowire is by using materials that are more nonlinear than silica; any of these alternative materials must then have a damage threshold that is high enough to sustain the power necessary for conversion.

The results of Lægsgaard’s calculations are not encouraging. Works like this are nevertheless important because they provide a clear picture that experimenters can use to orient their efforts and perhaps find the right breakthrough that will allow inexpensive and efficient SHG.

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